Going through your review I learnt that you have an account with ICICI Bank. My siuggestion will be go for the Demat account with ICICI Direct. You can always have your Trading Account with any other stock broking companies. The trading account is the account through which you trade and Demat is the account where the bought shares are parked.
According to me.. go for Anand Rathi Securities. They have excellent research-. You can depend on their research reports they are too good. Moreover they have a very competitive brokerage charges.. that can go down to 1p/10p for intraday / delivery respectively. However your brokerage charge depends on your amount of investment.
Best of Luck!!!!